Integral Methods in Nonlinear Dynamics of Systems

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This monograph presents an integral method for analysing the dynamic behaviour of nonlinear, non-stationary, and controlled systems. The method is based on the use of nonlinear integral inequalities to obtain new estimates for the norms of solutions and Lyapunov functions for the corresponding systems of differential equations of disturbed motion. The book consists of seven chapters. The first chapter establishes new bounds for solutions to ordinary and infinite systems of differential equations using nonlinear integral inequalities in pseudo-linear form. The second chapter studies the equations of disturbed motion based on new estimates of Lyapunov functions. Here, conditions are established for various types of motion boundedness, including the stability of coupled systems under initial and subsequent disturbances. The third chapter is devoted to polynomial systems, where variations of Lyapunov functions are used to derive conditions for stability and stabilisation of motion, including the analysis of the zero solution of systems with aftereffects. Chapter 4 applies nonlinear integral inequalities to nonlinear systems with interval initial conditions, and studies the stabilisation of systems with multiple controls. Chapter 5 focuses on quasilinear systems with fractional derivatives, establishing conditions for boundedness and Lagrange stability. Chapter 6 introduces an integral method for time-scale dynamic equations with fractional derivatives, offering new tools for stability and boundedness analysis. The final chapter studies equilibrium stability in a model of confrontation between two countries and alliances, using Lyapunov functions and integral inequalities to determine conditions for stable equilibrium and changes in weapon levels. Sample Chapter(s) Preface References Chapter 7: Equilibrium Stability under Nuclear Confrontation Contents: Preface About the Author Acknowledgements Novel Boundaries for Solutions of Nonlinear Systems with Applications Integral Estimates of Lyapunov Functions and Their Applications Stability and Stabilisation of Motion of Polynomial and Interval Systems Stabilisation of Motions of Interval Bilinear and Affine Systems Stability and Boundedness of Solutions to Fractional-like Equations Elements of Fraction-like Dynamics on the Time Scale Equilibrium Stability under Nuclear Confrontation Appendix A Appendix B References Index

Ordinary Differential Equations: Linear and Nonlinear Systems, Dynamical Systems and Applications (1版)

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【簡介】 The theory of ordinary differential equations is addressed in detail in this textbook, and is split into three sections: linear equations and systems, the general theory of nonlinear systems, and the theory of dynamical systems. These topics can be taken together or studied independently.In addition to standard materials on the theory of ordinary differential equations, this textbook specialises in covering non-standard materials related to this theory including the theory of linear equation and systems with holomorphic coefficients; Kneser’s theorem on the complexity of the set of solutions in the absence of uniqueness; the method of sub- and supersolutions for cooperative systems; and a detailed construction of the global bifurcation diagrams for some parametric classes of one-dimensional boundary value problems, which are pivotal for applications of the theory.This is a self-contained, rigorous treatment of ordinary differential equations that is complemented by a variety of illustrating examples of the theory in practice. Many of these examples are related to models in Physics and Applied Sciences, making them suitable for students in Physics, Chemistry, Engineering, Mathematical Biology, Economics and Ecology as well as in Mathematics. Each chapter contains exercises to test students’ understanding of the topic and concludes with some historical notes and further discussions.

Linear and Nonlinear Optimization using Spreadsheets (1版)

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【簡介】 The use of spreadsheets to obtain solutions to a diverse array of examples offers a reader-friendly way of addressing a topic (optimization) that can sometimes be viewed as intimidating. Many people are readily familiar with spreadsheets and how they work, yet are apt to be unaware of the incredible power of Excel for solving some rather complex optimization problems. A major goal of the book is to sell readers on why it is so important to understand optimization, and a large collection of examples for a wide range of business decision making areas (e.g., production planning and scheduling, workforce planning and scheduling, location and supply chain distribution, location of emergency services, assembly line balancing, vehicle routing, project scheduling, revenue management, advertising, product design, payout schedules, productivity measurement, investment portfolio management, sports league scheduling, ranking models, etc.) affords a practical mechanism for achieving that goal. Another important contribution of the book is that it provides coverage of the mechanics of some common yet sophisticated statistical methods (regression, logistic regression, discriminant analysis, factor analysis, and cluster analysis), which are often opaque to many users of such methods. 【目錄】 Introduction Optimization Examples in Prescriptive Analytics: Production Planning Workforce Planning Continuous Facility Location Discrete Facility Location Routing Problems Facility Layout Project Scheduling Marketing Finance Sports Optimization Examples for Multivariate Statistical Methods Used in Predictive and Descriptive Analytics: Regression Logistic Regression Linear Discriminant Analysis Factor Analysis Cluster Analysis